ATAR Notes: Forum
VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: Ematuro on February 27, 2011, 09:42:22 pm
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Okay could someone please sum this up for me:
What is the difference between these:
dilation by a factor of # from x-axis
dilation by a factor of # from y-axis
dilation by a factor of # along the x-axis
dilation by a factor of # along the y-axis
dilation by a factor of # in the x-axis
dilation by a factor of # in the y-axis
I always get dilations wrong! T_T
And also, is a dilation factor of 2 from the x-axis the same as a dilation factor of 1/2 from the y-axis or something?
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Id explain, its pretty basic. But doesnt your book have the explenations.
Y dilation is with the x. For example in y=(3x+2)+2, the dilation from the y axis is 1/3. You use the coefficient that is with x.
If it was (1/3x+2)=2, the dilation from y axis will be 3.
However, one like this: y=2(x+2)-2, is dilated from the x axis by a factor of 2. You simply use the number outside the brackets in this example. In a hyperbola or a truncus, it will be the numerator (unless it is 1, because 1 means no dilation).
And again in those two types of functions, the dilation from y axis will be the numbers together with x.
One example, though is one you should know.
If there you need to describe the dilation of this equation: y= 2(3x+2)^2-2, your answer will be 18. The 3 with x will be to the power of 2, which makes it 9, then you multiply with 2. Thats how you get 18. After that, you are not required to explain the dilation from y axis. You can basically say, there is a dilation from from the x axis by a factor of 18. But you do have to talk about the translations. Which are the basics.
Hope it helped.
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Id explain, its pretty basic. But doesnt your book have the explenations.
Y dilation is with the x. For example in y=(3x+2)+2, the dilation from the y axis is 1/3. You use the coefficient that is with x.
If it was (1/3x+2)=2, the dilation from y axis will be 3.
However, one like this: y=2(x+2)-2, is dilated from the x axis by a factor of 2. You simply use the number outside the brackets in this example. In a hyperbola or a truncus, it will be the numerator (unless it is 1, because 1 means no dilation).
And again in those two types of functions, the dilation from y axis will be the numbers together with x.
One example, though is one you should know.
If there you need to describe the dilation of this equation: y= 2(3x+2)^2-2, your answer will be 18. The 3 with x will be to the power of 2, which makes it 9, then you multiply with 2. Thats how you get 18. After that, you are not required to explain the dilation from y axis. You can basically say, there is a dilation from from the x axis by a factor of 18. But you do have to talk about the translations. Which are the basics.
Hope it helped.
thank you this helped me so much in understanding dilations, why are dilations so poorly documented